'Modeling' a sparkling flare?
Final (almost) result



I will not go trough all steps in detail as they aren't part of the question (animation, modeling this sparkling stick and such).

Particle system

Create IcoSphere and scale it to be a bit wider then stick and add to it Particle System.

Create another one and move it to another layer - you will use it as particle object.



Most important settings are:


Lifetime, short lifetime does not allow particles to bounce and long one will get all of them messy.
Emitter Geometry > Normal. This will give our particles initial speed.


The rest of them are just some little tweaks.

Do not forget to set Gravity 0 in Field Weights tab.

Collision system

This is the tricky devil.


Create IcoSphere (Subdivisions 2) go to Edit Mode and Wireframe view (Z).
Select all - A and hit CTRL+E then Edge Split.
Select all again and set Pivot Center to Individual Origins then scale it down little bit. You should get something like this:





Now you can duplicate it and make them smaller, bigger, with any rotation - as you like. Remember to set Pivot Center back again to Median Point.
Final step, still in Edit Mode add another IcoSphere and make it the biggest one. This will be boundry for our collision system.


My final setup looks like this:




  Creating collision system is the worst part, everything depends on it,
  so you must try to make it right. If you want sparkles to be bigger,
  make whole thing bigger, if you want them to be more round - scale
  down less after edge split, to have smaller holes between faces.


Go back to Object Mode and in Physics tab add Collision. Set Particles > Permeability to 0.3. This will allow particles to "break" collision system. You can set it to 0, then nothing (yup, almost) go trough.

Hide this object in Outliner and set it to not renderable. Eye and camera Icon.

Materials

We will need only two materials, for sparks (particles) and particle emitter. Select IcoSphere you've moved to another layer and add this node setup:



Select IcoSphere which is emitter for particles and add to it Transparent node with pure white color.

Motion Blur

Go to Render tab, check Motion Blur and set it to 1.10.

And that's it.

Here is .blend file with all animations: